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Current research projects

DFG Priority Programme 1962
DFG Priority Programme 1962 "Nonsmooth and Complementaritybased Distributed Parameter Systems"

Multiobjective Optimization of Non-Smooth PDE-Constrained Problems — Switches, State Constraints and Model Order Reduction

In almost all technical applications, multiple criteria are of interest – both during development as well as operation. Examples are fast but energy efficient vehicles and constructions that have to be light as well as stable. The goal in the resulting multiobjective optimization problems is the computation of the set of optimal compromises – the so-called Pareto set. A decision maker can then select an appropriate solution from this set. In control applications, it is possible to quickly switch between different compromises as a reaction to changes in the external conditions.

The Pareto set generally consists of infinitely many compromise solutions, its numerical approximation is therefore considerably more expensive than the solution of scalar optimization problems. This can quickly result in prohibitively large computational cost, particularly in situations where solutions to the underlying system are computationally expensive. For instance, this is the case when the system is described by a partial differential equation (PDE). In this context, surrogate models that can be solved significantly faster than classical numerical approximations by the finite element method are frequently used. In the case of non-smooth PDEs, reducing the computational cost is particularly important since these problems are often significantly more expensive to solve than smooth problems. However, the surrogate models introduce an approximation error intro the system, which has to be quantified and considered both in the analysis and the development of numerical algorithms. For non-smooth problems, literature on this topic is currently scarce.

The goal of this project is the development of efficient numerical methods to solve multiobjective optimization problems that are constrained by non-smooth PDEs. In the first step, optimality conditions for the non-smooth PDE-constrained problems will be derived, and the (hierarchical) structure of the Pareto sets will be analyzed. Building on this, algorithms for the computation of Pareto sets will be developed for these problems. The methods will be used for the optimization of problems with max-terms, contact problems, and time dependent hybrid and switched systems. In order to handle the numerical effort, reduced order modeling techniques – such as Reduced Basis, Proper Orthogonal Decomposition, and more recent approaches based on the Koopman operator – will be extended to the non-smooth setting. This requires the consideration of inexactness in the convergence analysis. Finally, the algorithms will be applied to several different problem settings in cooperation with other members of the Priority Programme.

SET CPS

Simultaneous Development and Testing of Cyber Physical Systems (CPS) using the example of autonomous electric vehicles (SET CPS)

dSPACE, e.GO Mobile, and the Institute of Industrial Mathematics Launch Research Project

Paderborn/Aachen, May 28, 2019. How can autonomous vehicles with electric drives be developed as examples of complex cyber-physical systems faster, more cost-effectively, and with lower resource consumption? And how can the safety of these vehicles on the road be increased? A team of researchers and developers from dSPACE, e.GO Mobile AG, and the Institute of Industrial Mathematics at the University of Paderborn started a research project a few weeks ago to answer this complex question. The project is funded by the German state of North Rhine-Westphalia (NRW) and the EU as part of the IKT.NRW lead market competition. The project, scheduled to run for 36 months, aims to simultaneously develop and test cyber-physical systems (CPS) using the example of an electric autonomous vehicle. It is abbreviated SET CPS according to its German title.

In vehicle development, trends such as automated driving and the development of alternative drives, such as battery-powered vehicles, are causing a sharp increase in the demands placed on the underlying systems. When these types of vehicles are developed, the aim is to optimize a large number of target parameters such as fuel consumption, range, and driving comfort, and to guarantee the safety of the system. Researchers and developers in the SET CPS project are now looking for new approaches to make the development processes for manufacturers and suppliers reliable and economical, and enable them to meet development times.

The project therefore aims to develop intelligent, simulation-based processes that improve and systematize the development and test process of complex vehicles and increase the degree of automation. For this purpose, design and testing are more closely interlinked to achieve a high level of quality even in the early development phases. The researchers also use the latest mathematical methods from multi-objective optimization, which is one of the core competencies of the Institute of Industrial Mathematics. This enables them to simultaneously achieve competing goals, such as energy efficiency, comfort, and costs, while ensuring the safety of the system. The plan is to integrate the new processes into the dSPACE tool chain and evaluate them using an example from e.GO vehicle development.

“As consortium leader of the project, our goal is to take the next step toward a one-stop development environment for autonomous vehicles," explained Dr. Rainer Rasche, Group Manager Test Automation at dSPACE. “The resulting tool chain enables the developer to adjust the parameters of an ECU to different, typical traffic situations and simultaneously test them in the simulated environments. This will enable our customers to accelerate their development."

Dr. Michael Riesener, Vice President Corporate Research at e.GO Mobile AG, said: “The simultaneous development and testing of new systems for our electric vehicles made possible by SET CPS also enables us to achieve fast development times and to design the vehicles with an even stronger focus on requirements. For this reason, we look forward to advancing the research project in cooperation with our partners."

About e.GO Mobile AG

e.GO Mobile AG was founded in 2015 by Prof Dr Günther Schuh as a manufacturer of electric vehicles. The more than 400 employees use the campus's unique network of research facilities and approximately 360 technology companies on the RWTH Aachen Campus. Highly agile teams work on a variety of cost-effective and customer-focused electric vehicles for short-haul traffic. e.GO Mobile AG is currently commissioning its new plant in Rothe Erde, Aachen, for series production.

www.e-go-mobile.com

About IFIM

The Institute of Industrial Mathematics was founded at the University of Paderborn to facilitate a direct transfer of knowledge from applied mathematics to business. Together with partners from industry, in particular small and medium-sized enterprises, they identify mathematical problems and develop efficient solutions that are based on the latest scientific findings. The interaction between science and industry can yield significant progress in scientific, economic, and technological terms.

About dSPACE

dSPACE develops and distributes integrated hardware and software tools for developing and testing electronic control units. As a one-stop supplier, dSPACE is a sought-after partner and solution provider in many development areas of the automotive industry, from electromobility to vehicle networking to autonomous driving. The company's customer base therefore includes virtually all major vehicle manufacturers and suppliers. dSPACE systems are also used in the aerospace and other industries. With more than 1,700 employees worldwide, dSPACE is headquartered in Paderborn, Germany; has three project centers in Germany; and serves customers through regional dSPACE companies in the USA, the UK, France, Japan, China, and Croatia.

For more information on the funding program, visit: https://www.leitmarktagentur.nrw/leitmarktwettbewerbe/ikt/

 

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